A comparison of non-iterative and iterative estimators of heterogeneity variance for the standardized mortality ratio

This paper continues work presented in B?hning et al. (2002b, Annals of the Institute of Statistical Mathematics 54, 827-839, henceforth BMSRB) where a class of non-iterative estimators of the variance of the heterogeneity distribution for the standardized mortality ratio was discussed. Here, these estimators are further investigated by means of a simulation study. In addition, iterative estimators including the Clayton-Kaldor procedure as well as the pseudo-maximum-likelihood (PML) approach are added in the comparison. Among all candidates, the PML estimator often has the smallest mean square error, followed by the non-iterative estimator where the weights are proportional to the external expected counts. This confirms the theoretical result in BMSRB in which an asymptotic efficiency could be proved for this estimator (in the class of non-iterative estimators considered). Surprisingly, the Clayton-Kaldor iterative estimator (often recommended and used by practitioners) performed poorly with respect to the MSE. Given the widespread use of these estimators in disease mapping, medical surveillance, meta-analysis and other areas of public health, the results of this study might be of considerable interest.     

A Nonparametric Estimator of Heterogeneity Variance with Applications to SMR‐ and Proportion‐Data

In this paper the situation of extra population heterogeneity is discussed from a analysis of variance point of view. We first provide a non‐iterative way of estimating the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself for Poisson and binomial counts. The consequences of the presence of heterogeneity in the estimation of the mean are discussed. We show that if the homogeneity assumption holds, the pooled mean is optimal while in the presence of strong heterogeneity, the simple (arithmetic) mean is an optimal estimator of the mean SMR or mean proportion. These results lead to the problem of finding an optimal estimator for situations not represented by these two extreme cases. We propose an iterative solution to this problem. Illustrations for the application of these findings are provided with examples from various areas.     

Cross‐sectional human immunodeficiency virus incidence estimation accounting for heterogeneity across communities

Accurate estimation of human immunodeficiency virus (HIV) incidence rates is crucial for the monitoring of HIV epidemics, the evaluation of prevention programs, and the design of prevention studies. Traditional cohort approaches to measure HIV incidence require repeatedly testing large cohorts of HIV‐uninfected individuals with an HIV diagnostic test (eg, enzyme‐linked immunosorbent assay) for long periods of time to identify new infections, which can be prohibitively costly, time‐consuming, and subject to loss to follow‐up. Cross‐sectional approaches based on the usual HIV diagnostic test and biomarkers of recent infection offer important advantages over standard cohort approaches, in terms of time, cost, and attrition. Cross‐sectional samples usually consist of individuals from different communities. However, small sample sizes limit the ability to estimate community‐specific incidence and existing methods typically ignore heterogeneity in incidence across communities. We propose a permutation test for the null hypothesis of no heterogeneity in incidence rates across communities, develop a random‐effects model to account for this heterogeneity and to estimate community‐specific incidence, and provide one way to estimate the coefficient of variation. We evaluate the performance of the proposed methods through simulation studies and apply them to the data from the National Institute of Mental Health Project ACCEPT, a phase 3 randomized controlled HIV prevention trial in Sub‐Saharan Africa, to estimate the overall and community‐specific HIV incidence rates.     

Some general points in estimating heterogeneity variance with the DerSimonian-Laird estimator

In this paper we consider estimating heterogeneity variance with the DerSimonian-Laird (DSL) estimator as typically used in meta-analysis. In its general form the DSL estimator requires inverse population-averaged study-specific variances as weights, in which case the estimator is unbiased. It has become common practice, however, to use estimates of the study-specific variances instead of their population-averaged versions. This can lead to considerable bias. Simulations illustrate these findings.     

Nonparametric estimation of natural selection on a quantitative trait using mark-recapture data

Assessing natural selection on a phenotypic trait in wild populations is of primary importance for evolutionary ecologists. To cope with the imperfect detection of individuals inherent to monitoring in the wild, we develop a nonparametric method for evaluating the form of natural selection on a quantitative trait using mark-recapture data. Our approach uses penalized splines to achieve flexibility in exploring the form of natural selection by avoiding the need to specify an a priori parametric function. If needed, it can help in suggesting a new parametric model. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters. We illustrate our approach using data for a wild population of sociable weavers (Philetairus socius) to investigate survival in relation to body mass. In agreement with previous parametric analyses, we found that lighter individuals showed a reduction in survival. However, the survival function was not symmetric, indicating that body mass might not be under stabilizing selection as suggested previously.     

Semiparametric estimation of the transformation model by leveraging external aggregate data in the presence of population heterogeneity

Leveraging information in aggregate data from external sources to improve estimation efficiency and prediction accuracy with smaller scale studies has drawn a great deal of attention in recent years. Yet, conventional methods often either ignore uncertainty in the external information or fail to account for the heterogeneity between internal and external studies. This article proposes an empirical likelihood-based framework to improve the estimation of the semiparametric transformation models by incorporating information about the t-year subgroup survival probability from external sources. The proposed estimation procedure incorporates an additional likelihood component to account for uncertainty in the external information and employs a density ratio model to characterize population heterogeneity. We establish the consistency and asymptotic normality of the proposed estimator and show that it is more efficient than the conventional pseudopartial likelihood estimator without combining information. Simulation studies show that the proposed estimator yields little bias and outperforms the conventional approach even in the presence of information uncertainty and heterogeneity. The proposed methodologies are illustrated with an analysis of a pancreatic cancer study.     

Understanding implications of detection heterogeneity in wildlife abundance estimation

Negative bias in mark-recapture abundance estimators due to heterogeneity in detection (capture) probability is a well-known problem, but we believe most biologists do not understand why heterogeneity causes bias and how bias can be reduced. We demonstrate how heterogeneity creates dependence and bias in mark-recapture approaches to abundance estimation. In comparison, heterogeneity, and hence estimator bias, is not as problematic for distance sampling and mark-resight methods because both techniques estimate detection probabilities based on a known quantity. We show how the introduction of a known number of individuals planted into a study population prior to a mark-recapture survey can reduce bias from heterogeneity in detection probability. We provide examples with simulation and an analysis of motion-sensitive camera data from a study population of introduced eastern wild turkeys (Meleagris gallopavo silvestris) of known size with a subset of telemetered birds. In choosing a method for abundance estimation, careful consideration should be given to assumptions and how heterogeneity in detection probability can be accommodated for each application.     

Genetic heterogeneity of residual variance in broiler chickens

Aims were to estimate the extent of genetic heterogeneity in environmental variance. Data comprised 99 535 records of 35-day body weights from broiler chickens reared in a controlled environment. Residual variance within dam families was estimated using ASREML, after fitting fixed effects such as genetic groups and hatches, for each of 377 genetically contemporary sires with a large number of progeny (> 100 males or females each). Residual variance was computed separately for male and female offspring, and after correction for sampling, strong evidence for heterogeneity was found, the standard deviation between sires in within variance amounting to 15–18% of its mean. Reanalysis using log-transformed data gave similar results, and elimination of 2–3% of outlier data reduced the heterogeneity but it was still over 10%. The correlation between estimates for males and females was low, however. The correlation between sire effects on progeny mean and residual variance for body weight was small and negative (-0.1). Using a data set bigger than any yet presented and on a trait measurable in both sexes, this study has shown evidence for heterogeneity in the residual variance, which could not be explained by segregation of major genes unless very few determined the trait.     

Nonparametric estimation for the three-stage irreversible illness-death model

In this paper, we present new nonparametric estimators of the stage-occupation probabilities in the three-stage irreversible illness-death model. These estimators use a fractional risk set and a reweighting approach and are valid under stage-dependent censoring. Using a simulated data set, we compare the behavior of our estimators with previously proposed estimators. We also apply our estimators to data on time to Pneumocystis pneumonia and death obtained from an AIDS cohort study.     

人文因素对省域环境污染影响的空间异质性估计

利用2013年全国31个省级行政区的截面数据,采用环境污染货币化方法估算了2013年中国省域环境污染损失,利用基于地理加权回归技术的STIRPAT模型,对人口规模、富裕程度、产业结构、城镇化和对外开放等人文因素对省域环境污染的影响进行了空间异质性估计,同时验证了EKC假说。主要结论如下:(1)2013年中国环境污染引起的经济损失为2812.48亿元。(2)各省域环境污染存在空间相关性和空间异质性,省域环境污染空间分布上呈现东高西低的格局。(3)人文因素对省域环境污染具有显著影响,人口和经济的增长及推进城镇化将加剧省域环境污染,而产业结构升级和扩大对外开放将有助于缓解省域环境污染。(4)人文因素对省域环境污染影响存在空间异质性。人口数量对省域环境污染的影响程度由西北向东南渐次增大;富裕程度对省域环境污染的影响由西向东梯次增大;产业结构对省域环境污染的影响由东向西逐渐增大;城镇化对省域环境污染的影响由西向东逐渐降低;对外开放对省域环境污染的影响由东向西逐渐增大。(5)基于现有样本的计算结果有条件地支持EKC假说。     

Selection for uniformity in livestock by exploiting genetic heterogeneity of residual variance

In some situations, it is worthwhile to change not only the mean, but also the variability of traits by selection. Genetic variation in residual variance may be utilised to improve uniformity in livestock populations by selection. The objective was to investigate the effects of genetic parameters, breeding goal, number of progeny per sire and breeding scheme on selection responses in mean and variance when applying index selection. Genetic parameters were obtained from the literature. Economic values for the mean and variance were derived for some standard non-linear profit equations, e.g. for traits with an intermediate optimum. The economic value of variance was in most situations negative, indicating that selection for reduced variance increases profit. Predicted responses in residual variance after one generation of selection were large, in some cases when the number of progeny per sire was at least 50, by more than 10% of the current residual variance. Progeny testing schemes were more efficient than sib-testing schemes in decreasing residual variance. With optimum traits, selection pressure shifts gradually from the mean to the variance when approaching the optimum. Genetic improvement of uniformity is particularly interesting for traits where the current population mean is near an intermediate optimum.     

Unbiased relatedness estimation in structured populations

Knowledge of the genetic relatedness between individuals is important in many research areas in quantitative genetics, conservation genetics, forensics, evolution, and ecology. In the absence of pedigree records, relatedness can be estimated from genetic marker data using a number of estimators. These estimators, however, make the critical assumption of a large random mating population without genetic structures. The assumption is frequently violated in the real world where geographic/social structures or nonrandom mating usually lead to genetic structures. In this study, I investigated two approaches to the estimation of relatedness between a pair of individuals from a subpopulation due to recent common ancestors (i.e., relatedness is defined and measured with the current focal subpopulation as reference). The indirect approach uses the allele frequencies of the entire population with and without accounting for the population structure, and the direct approach uses the allele frequencies of the current focal subpopulation. I found by simulations that currently widely applied relatedness estimators are upwardly biased under the indirect approach, but can be modified to become unbiased and more accurate by using Wright's F(st) to account for population structures. However, the modified unbiased estimators under the indirect approach are clearly inferior to the unmodified original estimators under the direct approach, even when small samples are used in estimating both allele frequencies and relatedness.